Amenability, Bilipschitz Maps, and the Von Neumann conjecture

Details Amenability, Bilipschitz Maps, and the Von Neumann conjecture Amenability, Bilipschitz Maps, and the Von Neumann conjecture

1997-04-05

arxiv.org/abs/math/9704202v1

Mathematics

Group Theory

AMS-LaTeX, 13 pages

Scientific paper

We determine when a quasi-isometry between discrete spaces is at bounded distance from a bilipschitz map. From this we prove a geometric version of the Von Neumann conjecture on amenability. We also get some examples in geometric groups theory which show that the sign of the Euler characteristic is not a coarse invariant. Finally we get some general results on uniformly finite homology which we will apply to manifolds in a later paper.

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